#31558: 數學題


20060705sean (pneumonoultramicroscopicsilico...)


S(x) := x(x + 1)/2
題目所求:找出所有a、b滿足
S(a) - S(b) = C
a(a+1)/2 - b(b+1)/2 = C
a^2 + a - b^2 - b = 2C
(a+0.5)^2 - (b-0.5)^2 = 2C
(a+b+1)(a-b) = 2C
把2C做因分,假設p、q (p > q)是2C的一組因分
a = (p + q - 1)/2
b = (p - q - 1)/2